An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of $12$ $12$ and the triangle has an area of $45$ $45$ . What are the lengths of sides A and B?

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Answer 1 · 2016-09-20T01:51:11

$9.605$ $9.605$

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ABC is an isosceles triangle. $\Rightarrow A = B$ $=> A=B$

Area $(A_{r}) = \frac{1}{2} \times b \times H$ $(A_r)=1/2 xx bxxH$

where b=base and h=height.

Given $A_{r} = 45 and C = 12$ $A_r=45 and C=12$

$\Rightarrow A_{r} = 45 = \frac{1}{2} \times 12 \times H$ $=> A_r=45=1/2xx12xxH$ ; (C=base=12)

$\Rightarrow H = \frac{45 \times 2}{12} = 7.5$ $=> H=(45xx2)/12=7.5$

$\Rightarrow A = B = \sqrt{{7.5}^{2} + 6^{2}} = \sqrt{92.25} = 9.605$ $=> A= B=sqrt(7.5^2+6^2)=sqrt92.25=9.605$

An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of 12 1212 and the triangle has an area of 45 4545 . What are the lengths of sides A and B?